Let z and w be complex numbers such that |z| = |w| = 1 and zw does not equal -1. Prove that

Question

(z + w) / (zw + 1) is a real number.

I have tried to rationalize the denominator and I got (z^2*w-z*w^2) / (zw)^2-1 but that got me nowhere. Can someone please help me!!!

Answer 1

a quick check on the related questions below shows that a quick check with google provides a solution at

http://math.stackexchange.com/questions/427663/prove-if-z-w-1-and-1zw-neq-0-then-zw-over-1zw-is-a-real